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As far as I know, there's no reason you can't put a dishwasher just about anywhere you like in a kitchen. It's usually next to the sink because it makes sense to put it there, as well as reduces the amount of plumbing necessary for the kitchen.

Practicality issues aside, there's a fair bit of extra work involved to do this.
Everything below assumes a USA location with regard to electrical. The rest should be fairly universal.

You'll have to run water lines from the sink over to the oven space to supply the dishwasher.

If your oven is gas, electric is fairly easy, as both the dishwasher and the oven use 120V, however, you'll have to properly deal with moving the gas line to the new oven location.

If the oven is electric you'll have more electric work, as the 240V oven line has to be safely moved to wherever your oven is going, and a 120V line will need to be run to the dishwasher. Note that, if you opt to use the plug-in method of powering your dishwasher, you cannot have the plug behind the dishwasher as you can with an oven.

In either case, it's best to move the circuit or outlet the dishwasher was on previously to the new location, as dishwashers are supposed to have their own dedicated circuit.

You'll need to replace the section of countertop that will be missing once the oven is moved. For best appearances, you may need to replace the smaller sections on either side of the oven with one large section.

I don't think you specifically need to remove the microwave/hood vent from over the range, but it may look odd. If you do, you may wish to replace the wall cabinets above the now-dishwasher with full-height ones (also not explicitly necessary as far as I know, but again it may look odd).

Overall, I'd venture if you're in the middle of doing a full kitchen remodel (as in, a cabinets-fully-removed level of remodeling), it's as good a time as any to rearrange the layout. Otherwise, it may be more time, effort, and money than it's worth.